This preview shows pages 1–2. Sign up to view the full content.
Please notice that the solution below is just a possible one. Any different solutions
which make sense are also welcomed.
In the stochastic case, the new model is as below:
Maximize
3
123
456
789
1
[1000(
)
750(
)
250(
)]
j
jj
jjj
j
j
P
yyy
=
++
+
+
∑
Suppose Scenario 1 refers to the normal water allocation, Scenario 2 the 10% higher
case and Scenario 3 the 40% lower case. Therefore,
0.5,
0.4,
0.1
PPP
=
==
.
And the constraints for
,1
,
2
,
3
;
1
,
2
9
j
i
yj
i
K
are
And for each i, 0
j
ii
yx
≤≤
.
The constraints for
i
x
are the same as the constraint 1, 3, 4, 5 in the textbook.
Solving this linear programming, we can derive the optimal planting decisions shown
in table below
Allocation (Acres)
Kibbutz
Crop
1
2
3
Sugar beets
100
180
130
Cotton
180
240
80
Sorghum
0
0
0
And the optimal watering decision under Scenario 1 is (80, 106.7, 71.7, 180, 240, 80,
0, 0, 0); under Scenario 2 is (100, 133.3, 84.2, 180, 240, 80, 0, 0, 0); under Scenario 3
is (0, 0, 21.7, 180, 240, 80, 0, 0, 0). The expected return is $63333.3.
Please notice here there is NOT only one optimal solution to this programming.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 SteinW.Wallace

Click to edit the document details